﻿using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Inspired.Euler
{
    /// <summary>
    /// In the 2020 grid below, four numbers along a diagonal line have been marked in red.
    /// 
    /// The product of these numbers is 26  63  78  14 = 1788696.
    /// 
    /// What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 2020 grid?
    /// </summary>
    public static class Problem011
    {
        /// <summary>
        /// What is the greatest product of four numbers on the same straight line in the 20 by 20 grid?
        /// </summary>
        /// <returns></returns>
        [EulerNeedsRefactor]
        [EulerProblem(11, Title = "What is the greatest product of four numbers on the same straight line in the 20 by 20 grid?")]
        public static long Solve()
        {
            int[][] numbers = new[]{
                new []{ 08, 02, 22, 97, 38, 15, 00, 40, 00, 75, 04, 05, 07, 78, 52, 12, 50, 77, 91, 08 },
                new []{ 49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 04, 56, 62, 00 },
                new []{ 81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 03, 49, 13, 36, 65 },
                new []{ 52, 70, 95, 23, 04, 60, 11, 42, 69, 24, 68, 56, 01, 32, 56, 71, 37, 02, 36, 91 },
                new []{ 22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80 },
                new []{ 24, 47, 32, 60, 99, 03, 45, 02, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50 },
                new []{ 32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70 },
                new []{ 67, 26, 20, 68, 02, 62, 12, 20, 95, 63, 94, 39, 63, 08, 40, 91, 66, 49, 94, 21 },
                new []{ 24, 55, 58, 05, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72 },
                new []{ 21, 36, 23, 09, 75, 00, 76, 44, 20, 45, 35, 14, 00, 61, 33, 97, 34, 31, 33, 95 },
                new []{ 78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 03, 80, 04, 62, 16, 14, 09, 53, 56, 92 },
                new []{ 16, 39, 05, 42, 96, 35, 31, 47, 55, 58, 88, 24, 00, 17, 54, 24, 36, 29, 85, 57 },
                new []{ 86, 56, 00, 48, 35, 71, 89, 07, 05, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58 },
                new []{ 19, 80, 81, 68, 05, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 04, 89, 55, 40 },
                new []{ 04, 52, 08, 83, 97, 35, 99, 16, 07, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66 },
                new []{ 88, 36, 68, 87, 57, 62, 20, 72, 03, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69 },
                new []{ 04, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 08, 46, 29, 32, 40, 62, 76, 36 },
                new []{ 20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 04, 36, 16 },
                new []{ 20, 73, 35, 29, 78, 31, 90, 01, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 05, 54 } };

            List<int> products = new List<int>();
            var horizontals =
                from x in Enumerable.Range(0, 16)  // start from the left, and stop four cells before the right edge
                from y in Enumerable.Range(0, 19)  // include all rows from top to bottom
                select (from offset in Enumerable.Range(0, 4)
                        select numbers[x + offset][y]);
            var verticals =
                from x in Enumerable.Range(0, 19)
                from y in Enumerable.Range(0, 16)
                select (from offset in Enumerable.Range(0, 4)
                        select numbers[x][y + offset]);

            var forwardDiagonals =
                from x in Enumerable.Range(0, 16)
                from y in Enumerable.Range(0, 16)
                select (from offset in Enumerable.Range(0, 4)
                        select numbers[x + offset][y + offset]);

            var reverseDiagonals =
                from x in Enumerable.Range(3, 16)
                from y in Enumerable.Range(0, 16)
                select (from offset in Enumerable.Range(0, 4)
                        select numbers[x - offset][y + offset]);

            return 
                new[]
                {
                    horizontals,
                    verticals,
                    forwardDiagonals,
                    reverseDiagonals  
                }
                .SelectMany(sequence => sequence)
                .Select(quadruplet => quadruplet.Product())
                .Max();
        }
    }
}
